olymmath

IR-TST 2014 Problem 12

  • Test 2

Consider nn segments in the plane which no two intersect and between their 2n2n endpoints no three are collinear. Is the following statement true? Statement: There exists a simple 2n2n -gon such that it's vertices are the 2n2n endpoints of the segments and each segment is either completely inside the polygon or an edge of the polygon.

Dataset text AI-MO AoPS. Quoted with source.

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